Analytic scaling solutions for cosmic domain walls

Mark Hindmarsh (Sussex University)

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Analytic scaling solutions for cosmic domain walls

High Energy Physics - Phenomenology · Submitted 16 May 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is shown that there are self-similar ``scaling'' solutions, for which one can in principle calculate many quantities of interest without recourse to numerical simulations.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.83 · mentions code or data availability 0.02.

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A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there are self-similar ``scaling'' solutions, for which one can in principle calculate many quantities of interest without recourse to numerical simulations. Here, the area density in the scaling regime is calculated in various backgrounds. Remarkably good agreement with numerical simulations is obtained.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context.	contribution 0.91	0.93	0.09	asserted 0.99
s1	It is shown that there are self-similar ``scaling'' solutions, for which one can in principle calculate many quantities of interest without recourse to numerical simulations.	result 0.89	0.88	0.53	asserted 0.94
s2	Here, the area density in the scaling regime is calculated in various backgrounds.	contribution 0.87	0.94	0.10	asserted 0.98
s3	Remarkably good agreement with numerical simulations is obtained.	result 0.98	0.90	0.36	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.76 · evidence from proof or derivation 0.99.

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The paper

Original abstract

A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there are self-similar ``scaling'' solutions, for which one can in principle calculate many quantities of interest without recourse to numerical simulations. Here, the area density in the scaling regime is calculated in various backgrounds. Remarkably good agreement with numerical simulations is obtained.

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References

Forward citations

Cited by 16 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

DW-genesis: baryon number from domain wall network collapse
hep-ph 2024-11 conditional novelty 7.0 of 10

Collapsing axionic domain walls can produce the baryon asymmetry via spontaneous baryogenesis, with a maximum yield set by the annihilation temperature, but minimal post-inflationary realisations suffer a suppression ...
Domain walls through different cosmologies
astro-ph.CO 2026-07 accept novelty 6.5 of 10

Domain-wall network area scales as S ≈ 2ξV/τ with ξ≈1.2 across cosmologies from dust to near-Minkowski, so the particle horizon—not H⁻¹—sets the correlation length and GW peak.
Axion Isocurvature Perturbations Survive the Scaling Evolution of Axion Domain Walls
hep-ph 2026-08 conditional novelty 6.0 of 10

Axion isocurvature perturbations survive domain-wall scaling and annihilation because the energy released when the walls collapse inherits the superhorizon correlations of the inflationary axion field.
Biased Domain Wall Networks and their Gravitational Waves
astro-ph.CO 2026-07 conditional novelty 6.0 of 10

Population-biased domain wall networks annihilate at T_ann ~ T_s B_s^0.8 and emit a single-broken-power-law gravitational-wave spectrum peaking near twice the Hubble scale.
Dynamical criterion for biased domain-wall formation
hep-ph 2026-06 unverdicted novelty 6.0 of 10

Derives dynamical criterion for biased domain wall formation by evaluating p_fv at freeze-out temperature T_fo, producing stricter condition than conventional static threshold and consistency condition T_fo > T_ann.

Show 11 more citing papers

Collapsing domain walls with $\mathbb{Z}_2$-violating coupling to thermalized fermions and their impact on gravitational wave detections
hep-ph 2025-01 conditional novelty 6.0 of 10

Thermal corrections from a Z2-violating Yukawa coupling alter domain-wall annihilation temperatures and can change predicted gravitational wave spectra by orders of magnitude.
Domain wall interpretation of the PTA signal confronting black hole overproduction
gr-qc 2023-06 conditional novelty 6.0 of 10

Domain wall networks that fit the pulsar timing array background also produce solar-mass primordial black holes, whose mergers would source a kilo-Hz gravitational wave background.
Kilobyte Cosmic Birefringence from ALP Domain Walls
hep-ph 2020-12 conditional novelty 6.0 of 10

ALP domain walls without strings produce a quantized cosmic birefringence: an isotropic rotation of about 0.21 c_gamma degrees plus an anisotropic spectrum peaking near multipole 100.
Gravitational Waves from Collapsing Domain Walls
astro-ph.CO 2010-02 conditional novelty 6.0 of 10

Lattice simulations of collapsing cosmic domain walls produce a broad gravitational-wave spectrum whose low-frequency edge may be detectable by planned interferometers if the symmetry-breaking scale is 10^10 to 10^12 GeV.
Ultralight scalar field domain walls and Galileo GNSS atomic clocks
astro-ph.CO 2026-11 accept novelty 5.0 of 10

A framework of false-alarm rate and detection efficiency analyses is developed to search for domain-wall crossings in Galileo satellite atomic clock data.
Axionic domain walls at Pulsar Timing Arrays: QCD bias and particle friction
hep-ph 2023-06 conditional novelty 5.0 of 10

QCD-induced friction on axion domain walls can push the network out of the scaling regime for axion masses above roughly 10 GeV, weakening but not eliminating the domain-wall interpretation of the PTA signal.
Study of gravitational radiation from cosmic domain walls
astro-ph.CO 2011-02 conditional novelty 5.0 of 10

Domain walls produce a nearly flat, slightly red-tilted gravitational wave spectrum between the Hubble scale at decay and the wall width, with the slope changing at both scales.
Evolution of String-Wall Networks and Axionic Domain Wall Problem
astro-ph.CO 2010-12 conditional novelty 5.0 of 10

Lattice simulations give a decay-time law for biased axion domain walls, tau_dec proportional to sqrt(m)/(N_DW xi eta^3), which is converted into a narrow allowed window for the bias parameter and the Peccei-Quinn scale.
DW-genesis: generating the baryon number from domain walls
hep-ph 2024-12 conditional novelty 4.0 of 10

Axionic domain walls coupled to lepton number can generate the baryon asymmetry through spontaneous baryogenesis at collapse, but the associated gravitational wave signal is too faint for planned detectors.
Signals of Inflationary Models with Cosmic Strings
astro-ph.CO 2011-06 accept novelty 3.0 of 10

A review of the observational signatures of cosmic strings produced at the end of inflation, concluding that CMB data already bound the string tension G-mu below roughly 10^-6, while the loop population and hence the ...
A review of gravitational waves from cosmic domain walls
hep-ph 2017-03 accept novelty 2.0 of 10

Unstable cosmic domain walls with tension between roughly 10^3 and 10^12 GeV and annihilation temperatures between 10^-2 and 10^9 GeV produce a stochastic gravitational wave background that pulsar timing arrays, LIGO,...

How the literature uses it

36 arXiv papers cite this in 60 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 43 sentences without a confident label

Builds on it 1 paper

Furthermore, extending the suppression of [ref] to the FV fraction and expanding for small $η$ leads to a power-law growth of $$ (with a prefactor that is quadratic in the bias) and in 3D it predicts $p=3$.

Biased Domain Wall Networks and their Gravitational Waves · Qualitative picture · 0.88

Uses its method or tool 1 paper

The fitting model Eq.([ref]) is inspired by field theory analysis [ref] that employs mean-field approximation method and Gaussian ansatz on the field probability distribution in the limit of a small bias term $ϵ≪1$.

Dynamics of Long-lived Axion Domain Walls and Its Cosmological Implications · Scaling Regime · 0.84

Uses its data or values 1 paper

The results demonstrated in Table I of Ref. [ref] in the case of three spatial dimensions correspond to the area parameter $ξ≈(0.85, 0.9, 1.0)$ in Minkowski space, RD and MD universe, respectively.

Domain walls through different cosmologies · Conclusions · 0.97

Compares with it 3 papers

In the former case we found that the ad-hoc fitting formulas of Coulson et al. [ref] provide a good fit to our simulations, in contrast to the formula deduced from the analytic model of Hindmarsh [ref] .

Effects of Biases in Domain Wall Network Evolution · Conclusions · 0.90
The method used in [ref] (which later inspired [ref] ) appears to be radically different from ours but it shares important ingredients.

Domain wall annihilation -- a QFT perspective · Discussion · 0.88
These results are reminiscent of the scaling $exp(-η^d)$, in $d+1$ dimensions, suggested by [ref] .

Collapsing Domain Wall Networks: Impact on Pulsar Timing Arrays and Primordial Black Holes · False Vacuum fraction · 0.90

Cites it as support 1 paper

The fact that the cosmic expansion is not crucial in the evolution of $ξ$ could be envisaged from the fact that DWs enter the scaling regime also in Minkowski space [ref] .

Domain walls through different cosmologies · Universality of scaling · 0.97

Cites it as background 8 papers

In the scaling regime number of domain walls in Hubble horizon stays nearly constant, sizes of domain and average curvature radius of domain walls are of order of Hubble horizon [ref] .

Stability of domain walls in models with asymmetric potentials · Duration of scaling regime · 0.86
The annihilation of simple $ℤ_2$ DW networks has been discussed before [ref] , both analytically and numerically (using discretized field theory simulations).

Domain wall annihilation -- a QFT perspective · Introduction · 0.95
Scaling solution. — For the white noise or thermal initial conditions, the DW network quickly converges to the scaling solution, where there is on average about one DW per the Hubble horizon [ref] , given by

Stability of domain wall network with initial inflationary fluctuations, and its implications for cosmic birefringence · Introduction · 0.81

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